House Speaker John A. Boehner said Thursday that the U.S. and its allies are “losing ground” to the terrorists in Iraq and demanded President Obama come up with a better strategy for the fight.

“We’re losing ground to ISIL in Iraq and frankly Syria as well,” the Ohio Republican said, using one of the acronyms for the terrorist movement. “It shouldn’t be a surprise to anyone. We’ve been operating without an overarching strategy to deal with this terrorist threat.”

Mr. Obama earlier this year submitted a request for Congress to officially authorize the war that he’s already been conducting for a year, through airstrikes in both Syria and Iraq and attempts to aid government forces in Iraq, to try to halt the advance of the Islamic State.

That request, which Mr. Boehner had repeatedly demanded be submitted, was criticized by lawmakers on Capitol Hill. Some said it went too far in allowing limited use of ground troops, while others, including Mr. Boehner, said it didn’t do enough to lay out a credible plan for stopping the terrorists.

But Congress has done little to advance its own proposals, which it ultimately has the power to do — and Mr. Boehner has taken heat for failing to lead the House toward a solution.

In the absence of new authority, Mr. Obama is free to fight the war on his own terms, citing powers he says he still has to combat al Qaeda under the 2001 use of force authorization.

Last month Mr. Boehner said it was still up to Mr. Obama to take the lead, and called on the president to scrap his proposal and send up a new authorization for the use of military force, or AUMF in Capitol-speak. The speaker repeated that call Thursday.

“You can’t have an AUMF that calls for less authority than the president has today under existing law,” Mr. Boehner said.